Multi-Active RIS-Assisted THz Cell-Free Systems: Spectral and Energy Efficiency Tradeoff

Reconfigurable intelligent surfaces (RISs) and cell-free massive multiple-input multiple-output (CF-mMIMO) are effective solutions for mitigating large path loss and inter-cell interference in terahertz (THz) systems. However, passive RISs are notably limited from double-fading attenuation, motivating the use of active RISs with power amplification to improve signal strength. In this paper, we investigate a multi-active RIS-aided wideband CF-mMIMO system for THz communications, considering low-resolution digital-to-analog converters (DACs) to optimize the spectral efficiency (SE)-energy efficiency (EE) tradeoff by adjusting precoding vectors and reflection coefficient response of the RISs, subject to power and minimum desirable per-user rate constraints. This leads to a highly complex and non-convex, multi-objective and fractional optimization problem. To solve it, we propose a tailored quadratic transformation to manage the fractional form. This allows decomposition into two subproblems, which are iteratively solved via a successive convex approximation algorithm to optimize the precoding vectors and active RIS reflection coefficients until convergence. Numerical results demonstrate that the proposed active RIS-aided CF-mMIMO system effectively addresses propagation loss and limited scattering in THz communication, achieving superior EE and SE compared to conventional passive RIS across diverse scenarios. Furthermore, the integration of low-resolution DACs shows significant improvement in EE while preserving satisfactory communication performance.